David Warner will get the call from heavily pregnant wife at some point this month but the opener isn't expecting it to come in Perth.
Warner will leave Sydney on Friday, linking up with Australia's ODI squad before the five-match series against India starts at the WACA on Tuesday.
Candice Warner is due to give birth to the married couple's second child later this month.
David Warner skipped Australia's one-day tour of Zimbabwe in 2014 to be with Candice when she gave birth to Ivy Mae.
Quick single: Warner adds spark to SCG draw
Warner will again put baby above ball but that shouldn't involve a cross-country dash next week.
"Fingers crossed it comes when it's due, that's later towards the end of this month," he said after scoring the fastest SCG Test ton ever.
"I'm just looking forward to playing the first couple of one-dayers and obviously I'll be by the phone waiting for that phone call.
"There's a red-eye (flight from Perth to Sydney).
"I'm really looking forward to the one-day series. India are going to be very challenging. We know that they always bring a good competitive team out here."
Watch: Warner lights up dull draw
During India's tour last year, Warner demanded India batsman Rohit Sharma "speak English" in a heated on-field spat at the MCG.
Warner has come a long way since then, to the point where he will lead the side should Smith sit out a game because of his knee or hip niggles.
"That's in the past and I've matured a lot," the opener said of the scrap with Sharma.
"I let my emotions take over there.
"Steve is still our captain and he's on the park. We don't have to worry about that until things happen, he's fit and ready to go."
Quick single: Windies opt to play safe, not for keeps
Smith reiterated his desire to play all five ODIs against India, noting the showers in Sydney had been an unwanted chance to rest.
"It's been really good," the 26-year-old said of the niggles he has nursed throughout summer.
"It's been a good week off for me.
"I haven't done anything. The body's fresh and ready to go and up for every game this summer hopefully."